Pith Number

pith:TOSZTFEG

pith:2010:TOSZTFEGB7YZ2RKHQLVPHBA6NR

not attested not anchored not stored refs pending

Factorization formulas for higher depth determinants of the Laplacian on the n-sphere

Yoshinori Yamasaki

arxiv:1011.3095 v1 · 2010-11-13 · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TOSZTFEGB7YZ2RKHQLVPHBA6NR}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T04:35:56.527708Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9ba59994860ff19d454782eaf3841e6c5f2f0768cc0e49a4bee9f7ace2d66e15

Aliases

arxiv: 1011.3095 · arxiv_version: 1011.3095v1 · doi: 10.48550/arxiv.1011.3095 · pith_short_12: TOSZTFEGB7YZ · pith_short_16: TOSZTFEGB7YZ2RKH · pith_short_8: TOSZTFEG

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/TOSZTFEGB7YZ2RKHQLVPHBA6NR \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 9ba59994860ff19d454782eaf3841e6c5f2f0768cc0e49a4bee9f7ace2d66e15

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9c1231d0db283d0713d3deaab94beb929a4ada29c1da50ebc91efe495edf3cac",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-11-13T03:32:14Z",
    "title_canon_sha256": "0f59f1f305f34c87d9f31ab5c4f067ce3a588123c5c3d58ad76c613af4f7aff7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.3095",
    "kind": "arxiv",
    "version": 1
  }
}